Deformable aircraft capability envelope data set construction and online accurate prediction method

Abstract

The invention discloses a deformable aircraft capability envelope data set construction and online accurate prediction method, and belongs to the technical field of aircraft guidance control. The prediction method comprises the following steps: firstly, carrying out initial state sampling and pulling deviation processing based on a nominal trajectory of an aircraft, and carrying out fitting processing on aerodynamic data of different shapes; aiming at each initial state, solving a reachable domain and a maximum residual speed by adopting a variable optimization target trajectory planning method, and generating capability envelope data of the aircraft in the initial state; and based on the capability envelope data, establishing and training a deformable aircraft capability envelope online prediction model, and predicting the maximum residual speed of the aircraft in a specified initial state and a target position. Through the application of the method, the prediction efficiency can be greatly improved under the condition of low precision loss, and missile-borne application requirements are met.

Description

Technical Field

[0001] The invention relates to a deformable aircraft capability envelope data set construction and an online accurate prediction method, belonging to the technical field of aircraft guidance and control. Background Art

[0002] With the development of intelligent technology, deformation technology, decision optimization and advanced control theory, advanced aerospace vehicles are constantly expanding and extending in terms of flight style, mission capability, comprehensive performance and other aspects. In recent years, variable shape aircraft have gradually become a research hotspot. Such aircraft can autonomously change their own shape structure according to flight requirements, so that the mission profile in different flight stages can maintain the optimal flight state, which greatly enhances the aircraft's adaptability to the environment and multi-tasks. On this basis, the future complex, highly dynamic flight environment and diverse mission requirements put forward higher requirements for the online decision-making ability of aircraft. For example, when the aircraft is flying according to the pre-set trajectory, due to the discovery of sudden obstacles, the aircraft takes maneuvering to avoid them, resulting in deviation from the original trajectory, or there is a need to change the mission target online, the aircraft needs to quickly predict its future flight capability envelope, flexibly select the appropriate landing point and aerodynamic configuration, and complete the flight mission through online trajectory replanning. Therefore, it is urgent to develop an online accurate prediction method for the capability envelope of deformable aircraft to provide a basis for subsequent online mission planning, target allocation decision-making, etc.

[0003] At present, there are two main methods for predicting the capabilities of aircraft: analytical calculation method and numerical integration method. The analytical calculation method uses analytical algorithms to predict the state of the aircraft, with a small amount of calculation, but it often requires various simplifications of the state equation. Since the density and pressure of the atmosphere are exponentially distributed in the height direction, the aircraft has strong nonlinear dynamic characteristics, which makes it difficult to linearize the state equation. Therefore, the analytical method has weak applicability and poor accuracy. Numerical integration methods can be roughly divided into two categories: direct method and indirect method. The direct method is based on discretizing the control variables or state variables on a set of nodes, converting the optimal control problem into a nonlinear programming (NLP) problem, and the obtained NLP problem can usually be solved using a standard NLP solver. Among them, the pseudo-spectral (PS) method is derived from the spectral method. This method is usually used to solve fluid dynamics problems and usually has a faster convergence speed than other direct methods. The pseudo-spectral method is used for trajectory optimization and capability prediction, and the calculation accuracy is relatively ideal, but it requires multiple solutions to multi-constrained optimization problems under different horizontal and vertical ranges, which has a large amount of calculation and is difficult to achieve online prediction. With the development of artificial intelligence technology, the combination of intelligent algorithms and numerical methods, and the use of the powerful nonlinear representation ability of intelligent models to learn the implicit mapping relationship of data can avoid solving optimization problems and directly obtain capability prediction results, thereby greatly improving computing efficiency with a small loss of accuracy and meeting the needs of online aircraft applications. At present, this part of the research is still relatively lacking in the construction of a data set with sufficient accessibility capability envelope, the generalization of the model to multiple scenarios, and the adaptability to deformable aircraft, and further research is needed. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, propose a deformable aircraft capability envelope data set construction and online accurate prediction method, obtain the maximum residual speed of the aircraft under the current state and target position, and can greatly improve the efficiency of aircraft terminal flight capability prediction under low precision loss conditions.

[0005] The technical solution of the present invention is:

[0006] A method for constructing a deformable aircraft capability envelope data set and accurately predicting it online includes:

[0007] S1: sampling the initial velocity of the nominal trajectory segment of the deformable aircraft to be predicted, and sampling the trajectory height corresponding to the initial velocity to obtain a number of initial heights under all the deviation states; fitting the aerodynamic data of each shape of the aircraft to obtain the aerodynamic function of the angle of attack, Mach number and altitude;

[0008] S2: determining a set of calculation conditions, including but not limited to the aerodynamic configuration, initial speed, and initial altitude of the aircraft;

[0009] S3: Based on the dynamic model of the aircraft, according to the calculation conditions and aerodynamic functions, the maximum longitudinal range, minimum longitudinal range and maximum lateral range of the flight are solved under the constraints of terminal speed and altitude, and the reachable domain represented by relative longitude and latitude is generated;

[0010] S4: performing the following processing on each group of calculation conditions determined in step S1: traversing the relative longitude and latitude of points in the reachable domain, taking the relative longitude and latitude as the terminal position constraint, solving the trajectory with the optimal terminal residual speed, and obtaining the capability envelope data of the aircraft under the calculation conditions, the capability envelope data including but not limited to the aircraft aerodynamic configuration, initial speed, initial altitude, target relative longitude, target relative latitude and the corresponding maximum residual speed of the aircraft;

[0011] S5: Construct a capability envelope data set, perform feature selection and labeling on the capability envelope data, form a supervision data set in a unified format, and divide it into a training data set and a test data set;

[0012] S6: Based on the training data set, establish and train an online prediction model for the capability envelope of a deformable aircraft, and perform supervised learning;

[0013] S7: Based on the test data set, select test indicators and test the trained online prediction model of the deformable aircraft capability envelope;

[0014] S8: Obtain the real-time speed, altitude, relative distance to the target and the angle of attack to the target of the deformable aircraft, input them into the online prediction model of the capability envelope of the deformable aircraft that has passed the test, and predict the maximum remaining speed of the aircraft in this state and target position.

[0015] Furthermore, the Gauss pseudo-spectral method is used to calculate the reentry reachable domain. The angle of attack profile is not fixed. The angle of attack and the roll angle are simultaneously used as variables to be optimized to generate the reachable domain, which is as follows:

[0016] In the polar coordinate system, the latitude and longitude of the starting point of the aircraft are both 0, and the longitude and latitude of the end point describe the longitudinal and lateral range of the aircraft respectively. The reentry reachable domain calculation method based on the Gauss pseudospectral method first solves the maximum and minimum longitudinal ranges L max and L min ; Then from the longitudinal L max -ΔL, solve the two maximum horizontal range problems respectively, and reduce the vertical range ΔL successively until it reaches L min , and obtain the maximum lateral trajectory under different longitudinal conditions; finally, the reentry reachable area of ​​the aircraft represented by relative longitude and latitude is obtained.

[0017] Furthermore, before the reentry reachable domain calculation method based on the Gauss pseudospectral method is calculated, when setting the parameters of the pseudospectral method, the Coriolis acceleration term and the involved acceleration term in the differential equation are not 0, and the latitude variation range of the northern hemisphere trajectory is set to [-2°, 90°], and the latitude variation range of the southern hemisphere trajectory is set to [-90°, 2°].

[0018] Furthermore, the capability envelope data is calculated based on the Gauss pseudo-spectral method. The longitude and latitude of the points in the traversable domain are taken as terminal constraints. The maximum terminal residual speed is taken as the variable to be optimized to find the optimal trajectory of the terminal residual speed, that is, to obtain the capability envelope data of the aircraft at the current initial altitude and initial speed.

[0019] Furthermore, feature selection and labeling are performed on the capability envelope data to form a unified format of supervision data set. The input features of the supervision data set are the initial speed of the aircraft, the initial altitude, the relative distance between the aircraft and the target, and the direction angle between the aircraft and the target. The output feature is the maximum residual speed of the aircraft under the above initial state and target position.

[0020] Among them, the relative longitude and relative latitude in the capability envelope data are extracted for features:

[0021]

[0022] R=R e ·C

[0023]

[0024] In the formula, R e is the radius of the earth, λ is the relative longitude, is the relative latitude; R is the relative distance, and A is the direction angle, which are used as input features.

[0025] Furthermore, the aerodynamic data of each shape of the aircraft is fitted, specifically:

[0026] The aerodynamic data used are the basic aerodynamic data without rudder deflection, and the sideslip angle is zero, and the lateral force of the plane-symmetrical aircraft is zero;

[0027] The fitting process is as follows: decompose the axial force coefficient and the normal force coefficient into the drag coefficient and the lift coefficient, and then use a cubic polynomial to fit them as a function of the Mach number and the angle of attack; fit the axial force coefficient increment as a function of the Mach number and the altitude; and finally obtain the aerodynamic function of the angle of attack, Mach number and altitude.

[0028] Furthermore, the initial velocity sampling is performed on the nominal trajectory segment of the predicted deformable aircraft. The applicable speed range of different aerodynamic configurations is considered when selecting the trajectory velocity points. For the configuration that fails to cover all flight trajectory segments, its maximum allowable speed and the corresponding height on the nominal trajectory are taken as the initial state point.

[0029] Furthermore, based on the polar coordinate system, the dynamic model of the aircraft is established, and the constraints satisfying the stagnation point heat flux density, overload constraints and dynamic pressure constraints are given. The above constraints are specifically:

[0030]

[0031] In the formula, is the heat flux density, is the heat flow calculation parameter, R N is the stagnation radius, ρ is the atmospheric density, ρ0 is the standard atmospheric density at sea level, ν is the speed of the aircraft relative to the earth, V c is the first cosmic velocity, is the maximum heat flux density that the aircraft can withstand; g0 is the earth's gravitational acceleration, n max is the maximum aerodynamic overload that the aircraft can withstand; q is the dynamic pressure, q max is the maximum dynamic pressure; L and D are the lift acceleration and drag acceleration of the aircraft respectively.

[0032] Furthermore, an online prediction model of the capability envelope of a deformable aircraft is established by using any of the supervised learning algorithms including but not limited to support vector machines, decision trees, multi-layer perceptrons, and deep neural networks. The initial speed, initial altitude, relative distance between the aircraft and the target, and the heading angle between the aircraft and the target are used as model inputs, and the maximum remaining speed of the aircraft in the above initial state and target position is used as the model output.

[0033] Furthermore, the trained online prediction model of the capability envelope of the deformable aircraft is tested, and the test indicators are selected as key indicators for measuring the regression model, including but not limited to the mean absolute error, root mean square error, square correlation coefficient, and determination coefficient.

[0034] The advantages of the present invention compared with the prior art are:

[0035] (1) The present invention designs a method for generating aircraft capability envelope data based on variable optimization target trajectory planning. First, the maximum longitudinal range, minimum longitudinal range and maximum lateral range of the flight are solved under the constraints of fixed terminal speed and altitude. Secondly, the flight trajectory with the optimal terminal residual speed is traversed within the range of longitudinal and lateral ranges to ensure that the generated capability envelope data meets the requirements of accessibility and sufficiency.

[0036] (2) The present invention designs an online accurate prediction method with initial velocity, initial altitude, relative distance and firing angle as characteristic inputs. The relative information is used to characterize the position relationship between different missiles and targets. The algorithm can adapt to the dynamic changes of different aerodynamic configurations of the aircraft, the initial flight state, and the longitude and latitude of the target.

[0037] (3) Compared with traditional optimization methods, the online accurate prediction method of the aircraft capability envelope designed by the present invention can greatly improve the prediction efficiency under low precision loss conditions and meet the requirements of missile-borne applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0039] Figure 1 It is a block diagram of the method for constructing a deformable aircraft capability envelope data set and online accurate prediction of the invention;

[0040] Figure 2 A flow chart of the method for constructing a deformable aircraft capability envelope data set and online accurate prediction of the invention;

[0041] Figure 3 This is a schematic diagram of trajectory data preprocessing according to an embodiment of the present invention;

[0042] Figure 4 A schematic diagram of the maximum horizontal range problem under different vertical ranges in the generation of a reachable domain according to an embodiment of the present invention;

[0043] Figure 5 Generate a calculation flow chart for the reachable domain of an embodiment of the present invention;

[0044] Figure 6 Generate a result graph of the reachable domain under a set of working conditions of an embodiment of the present invention;

[0045] Figure 7 A result diagram of capacity envelope data generation under a set of working conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0046] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0047] The present invention proposes a method for constructing a deformable aircraft capability envelope data set and an online precise prediction method. The capability envelope data meets the requirements of accessibility and sufficiency. The model has good generalization ability under changes in parameters such as initial flight state, relative target position, and aerodynamic configuration, and achieves a significant improvement in the efficiency of aircraft terminal flight capability prediction under low precision loss conditions.

[0048] This method is Figure 2 As shown, including:

[0049] S1: Data preprocessing, including trajectory data and aerodynamic data preprocessing.

[0050] Firstly, the nominal trajectory segment of the aircraft to be predicted is selected, the initial velocity is sampled at a certain interval, and the trajectory height corresponding to the initial velocity is sampled offset to improve the generalization ability of the model for different initial flight states; then, the aerodynamic data of each shape of the aircraft are fitted with high-order polynomials to support the subsequent generation of capability envelope data.

[0051] S2: Determine a set of calculation conditions, including but not limited to the aerodynamic configuration of the aircraft, the initial speed, and the initial altitude.

[0052] S3: Generate a reachable domain, and for a set of calculation conditions determined in step S2, solve the maximum longitudinal range, minimum longitudinal range and maximum lateral range of the flight under fixed terminal speed and altitude constraints.

[0053] S4: Generate capability envelope data, traverse the longitude and latitude of the points in the reachable domain generated in step S3, and solve the trajectory with the optimal terminal residual speed as the terminal position constraint to obtain the aircraft capability envelope data under this working condition.

[0054] S5: Determine whether the capacity envelope data in all the pulling states in step 1 have been completed. If not, repeat steps S2 to S4; if completed, proceed to step S6.

[0055] S6: Construct a capability envelope data set, complete feature selection and labeling for all capability envelope data obtained in the above steps, and form a supervised data set in a unified format. Randomly divide the training data and test data according to a certain ratio.

[0056] S7: Establish and train an online prediction model for the capability envelope of a deformable aircraft, select an appropriate supervised learning algorithm, and use the training data to complete the training.

[0057] S8: Test the online prediction model of the deformable aircraft capability envelope, select test indicators such as accuracy and computational efficiency, and complete the test using test data.

[0058] S9: Obtain the real-time speed, altitude, relative distance to the target and the angle of attack to the target of the deformable aircraft, input them into the online prediction model of the capability envelope of the deformable aircraft that has passed the test, and predict the maximum remaining speed of the aircraft in this state and target position.

[0059] Based on this method, a prediction system is established. Figure 1 As shown, it includes a data preprocessing module, a capability envelope data generation module, a data set construction module, a model training module, and a model reasoning module.

[0060] The data preprocessing module performs initial state sampling and deflection processing based on the nominal trajectory of the aircraft, and fits the aerodynamic data of different shapes.

[0061] The capability envelope data generation module uses a trajectory planning method with a variable optimization objective to solve the reachable domain and the maximum residual speed for each initial state, and generates the capability envelope data of the aircraft in the initial state.

[0062] The dataset construction module repeats the capability envelope data generation process until the capability envelope data of the aircraft in all pulling and deflecting states are obtained, and feature selection and label annotation are completed to construct a deformable aircraft capability envelope dataset.

[0063] The model training module selects a suitable machine learning algorithm for training according to the training data set randomly divided in a certain proportion, and stops iterating until the training loss converges to obtain an online prediction model of the deformable aircraft capability envelope.

[0064] The model reasoning module tests the accuracy and computational efficiency of the trained model based on a test data set that is randomly divided into a certain proportion, and verifies the generalization ability of the model under changes in parameters such as initial flight state, relative target position, and aerodynamic configuration.

[0065] The present invention is further described by examples:

[0066] Figure 3 It is a schematic diagram of trajectory data preprocessing in step S1 of the present invention. According to the actual situation, the initial speed deviation processing is performed at 400 / 300 / 200m / s. The initial height is the trajectory height corresponding to the speed. The upper and lower deviation range is ±12km, and the points are taken at 2.5km. It should be noted that when selecting trajectory speed points, the applicable speed range of different aerodynamic configurations should be considered. For configurations that fail to cover all flight trajectory segments, the most initial state point of the maximum allowable speed and the corresponding height on the nominal trajectory should be taken.

[0067] In this embodiment, the aerodynamic data preprocessing of step S1 only uses the basic aerodynamic data without rudder deflection, and the sideslip angle is zero, and the lateral force of the plane-symmetric aircraft is zero. Therefore, the aerodynamic data calculation formula in the center of mass coordinate system of each configuration is:

[0068] Cx=Cx(BASIC)+△Cx(height correction)

[0069] Cy=Cy(BASIC)

[0070] Only the aerodynamic coefficients are considered to be related to the Mach number and angle of attack, and the axial force coefficient increment is only related to the Mach number and altitude. The axial force and normal force coefficients are first decomposed into the drag coefficient and lift coefficient, and then a cubic polynomial is used to fit them as a function of the Mach number and angle of attack. The axial force coefficient increment is first fitted as a function of the Mach number and altitude, and in actual calculations, it is decomposed into the drag coefficient increment and the lift coefficient increment according to the current angle of attack, and then added to the original drag coefficient and lift coefficient to obtain the total aerodynamic coefficient.

[0071] Before generating the reachable domain in step S3, the aircraft dynamics model should be constructed, including:

[0072] The dynamic model converted in the polar coordinate system is used, and its variables are also the variable values ​​in the polar coordinate system. The reason is that in the polar coordinate system, the longitude and latitude of the starting point of the aircraft are both 0, and the longitude and latitude of the end point describe the longitudinal and lateral range of the aircraft respectively. Using these characteristics, the parameter range in the trajectory planning problem can be easily calibrated and the trajectory planning algorithm can be simplified.

[0073] In the polar coordinate system, the dynamic equation of the aircraft can be derived as shown below:

[0074]

[0075] Where v is the velocity of the aircraft relative to the earth, θ is the local velocity inclination. ψ is the velocity azimuth, defined as the angle between the velocity vector and the true north direction, and clockwise is positive. r is the distance from the center of mass of the aircraft to the center of the earth. λ and g′ are the longitude and latitude in the polar coordinate system. r is the gravitational acceleration component. The associated acceleration term corresponding to the rotation of the earth is The Coriolis acceleration term is C θ , C ψ , which can be expressed as:

[0076] C ψ =2ω e (sinφ-cosψtanθcosφ)

[0077]

[0078] C θ =2ω c sinψcosφ

[0079]

[0080] σ is the roll angle, L and D are the lift acceleration and drag acceleration of the aircraft respectively. The calculation formula is:

[0081]

[0082] Where ρ is the atmospheric density, M is the mass of the aircraft, S is the reference area, and C L and C D They are the lift coefficient and drag coefficient respectively, both of which are related to the angle of attack α.

[0083] In addition to satisfying the above dynamic model, the aircraft also needs to satisfy the stagnation point heat flux density constraint, overload constraint, and dynamic pressure constraint during gliding, as shown in the following formula:

[0084]

[0085] In the formula, is the heat flux density, is the heat flow calculation parameter, R N is the stagnation radius, ρ0 is the standard atmospheric density at sea level, V c is the first cosmic velocity, is the maximum heat flux density that the aircraft can withstand. g0 is the earth's gravitational acceleration, n max is the maximum aerodynamic overload that the aircraft can withstand. q is the dynamic pressure, q max is the maximum dynamic pressure.

[0086] Step S3 generates the reachable domain using a Gauss pseudo-spectral method based on the reentry reachable domain calculation method. The angle of attack profile is not fixed, and the angle of attack and the roll angle are simultaneously used as variables to be optimized for optimization. The reentry reachable domain problem can be expressed as a maximum lateral range optimization problem under different longitudinal range conditions. In the polar coordinate system, the lateral range of the landing point can be represented by latitude:

[0087]

[0088] In the formula, is the latitude of the end point in the polar coordinate system. Figure 4 is a schematic diagram of the maximum horizontal range problem under different vertical ranges in the reachable domain generation provided by an embodiment of the present invention, such as Figure 4 As shown, L set is the set vertical range, λ pf To convert the longitude of the end point in the polar coordinate system, the two values ​​are equal. setAs a terminal constraint, by changing L set The maximum horizontal trajectory under different longitudinal conditions is obtained by changing the polar coordinate system. All trajectories are called northern hemisphere trajectories, and vice versa. When setting the parameters of the pseudo-spectral method, the influence of the earth's rotation is taken into account, that is, the Coriolis acceleration term and the involved acceleration term in the differential equation are not 0, and the latitude range of the northern hemisphere trajectory is set to [-2°, 90°], and the latitude range of the southern hemisphere trajectory is set to [-90°, 2°]. Solving the maximum horizontal range problem under the above different longitudinal ranges can obtain the effective reachable domain. However, in actual simulation, it is also necessary to determine the maximum and minimum longitudinal ranges (L max and L min ) in order to determine L set Therefore, the final planning process is as follows Figure 5 As shown, first solve the maximum and minimum longitudinal ranges and calibrate L max and L min The specific value of max -ΔL, solve the two maximum horizontal range problems respectively, and reduce the vertical range ΔL successively until it reaches L min ; Finally, the re-entry domain of the aircraft can be obtained.

[0089] At the same time, under ideal conditions in the relative coordinate system, the flight trajectory is symmetrical about the longitude line of the polar coordinate system, that is, the absolute values ​​of the maximum longitudinal ranges corresponding to the positive and negative heading angles are equal, and the absolute value changes of the flight state and control quantities are also the same. Therefore, it is only necessary to solve the reachable domain of the positive longitude, and the negative longitude is symmetrical. Figure 6 is a graph of the reachable domain generation results under a set of working conditions provided by an embodiment of the present invention, in which φ p represents the relative latitude in the polar coordinate system, λ p Represents the relative longitude in the polar coordinate system. This result shows the accessible domain form of positive longitude, and negative longitude is about φ p =0° symmetric.

[0090] The generation of capability envelope data in step S4 also uses the Gauss pseudo-spectral method, and the other conditions are the same as step S3, but the objective function to be optimized is changed to the maximum terminal residual speed, and the longitude and latitude of the points in the reachable domain are traversed as the terminal constraints. The trajectory with the optimal terminal residual speed is solved to obtain the capability envelope data of the aircraft at this initial height and initial speed state. In the actual simulation, in order to fully find the boundary, a certain expansion calculation is performed outside the reachable domain, and finally the data with residual speeds far less than the expected terminal speed at some points in the periphery are eliminated. Figure 7 A graph of capacity envelope data generation results under a set of working conditions provided in an embodiment of the present invention. The capacity envelope data generated by the method provided by the present invention meets the requirements of accessibility and sufficiency.

[0091] The capability envelope data set constructed in step S6 requires feature selection and labeling. The capability envelope data directly obtained in step 4 includes but is not limited to the aerodynamic configuration of the aircraft GX, initial speed v, initial altitude h, target relative longitude λ, target relative latitude In order to improve the generalization ability of the model for different target longitudes and latitudes, the present invention proposes to characterize the position relationship between different projectiles and targets through relative information, that is, converting the relative longitude and latitude into relative distance R and firing angle A according to the following formula as feature input:

[0092]

[0093] R=R e ·C

[0094]

[0095] Where R e is the radius of the earth. In addition, since the trajectory planning solutions under different aerodynamic configurations are quite different, in order to reduce the difficulty of training and improve the prediction accuracy, the datasets under different aerodynamic configurations are constructed respectively to train the prediction models suitable for different aerodynamic configurations. Finally, the constructed capability envelope dataset is expressed in a unified format as Where D GX represents the capability envelope data set under a certain aerodynamic configuration, The four-dimensional input features selected and related to the capability envelope are [aircraft initial speed v, initial height h, relative distance between aircraft and target R, and angle A between aircraft and target]. It is the maximum remaining speed of the aircraft at the initial state and target position obtained in step S4. The ratio of training and test data sets is 8:2.

[0096] The supervised learning algorithm in step S7 includes but is not limited to support vector machine (SVM), decision tree (Decision Tree), multi-layer perceptron (MLP), deep neural network (DNNs), etc. In the embodiment provided by the present invention, a machine learning algorithm based on SVM support vector machine is specifically adopted. The regression plane that needs to be determined by the regression algorithm based on SVM can be expressed as:

[0097] t(x)=w T Φ(x)+b

[0098] in, represents the normal vector of the hyperplane, represents the intercept of the hyperplane, and both are parameters to be estimated. The nonlinear transformation of the input features is contained in Φ(·), which can be achieved by a kernel trick. In the embodiment provided by the present invention, the kernel function is a Gaussian kernel function.

[0099] The ε-insensitive function is introduced in the regression algorithm, which is expressed as:

[0100]

[0101] The SVM-based regression algorithm aims to solve the following optimization problem:

[0102]

[0103] Among them, the slack variable ξ i , It is used to represent the empirical risk brought by samples that do not meet the margin constraint. The penalty factor C is used to control the trade-off between minimizing training error and model complexity.

[0104] The optimization problem in the above formula can be transformed into a Lagrangian dual problem and solved using methods such as quadratic programming (QP) and sequential minimum optimization (SMO). The optimal Lagrangian multiplier is obtained After that, the final online prediction model of capability boundary can be expressed as:

[0105]

[0106] where k(x,x i )=Φ(x) T Φ(x i ) represents the kernel function. According to the KKT condition, only some of them meet or The support vector contributes to the final decision, so in practical applications SVM has good robustness and sparsity, which can reduce the demand for storage and achieve fast model prediction.

[0107] The test indicators in step S8 are the key indicators commonly used to measure regression models: mean absolute error (MAE), root mean square error (RMSE), squared correlation coefficient (Squared Correlation Coefficient), determination coefficient (R 2). Among them, the mean absolute error refers to the average value of the absolute error between the model prediction value and the true value; the root mean square error refers to the sample standard deviation of the difference between the model prediction value and the true value; the square correlation coefficient uses the Pearson correlation coefficient, which can be used to measure the degree of linear correlation between two variables; the determination coefficient refers to the proportion of the dependent variable variation that can be explained by the independent variable to the total variation, which can be used to measure the goodness of fit of the regression model. In terms of numerical results, the smaller the mean absolute error and the root mean square error, the closer the square correlation coefficient and the determination coefficient are to 1, indicating that the regression performance of the model is better.

[0108] The mean absolute error is calculated as:

[0109]

[0110] The formula for calculating the root mean square error is:

[0111]

[0112] The formula for calculating the square correlation coefficient is:

[0113]

[0114] The formula for calculating the coefficient of determination is:

[0115]

[0116] Among them, y i Represents the model prediction value, y i represents the true value, Represents the sample mean.

[0117] The above-described embodiments are only preferred specific implementations of the present invention. Common changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for constructing a deformable aircraft capability envelope data set and online accurate prediction, characterized in that: include: S1: sampling the initial velocity of the nominal trajectory segment of the deformable aircraft to be predicted, and sampling the trajectory height corresponding to the initial velocity to obtain a number of initial heights under all the deviation states; fitting the aerodynamic data of each shape of the aircraft to obtain the aerodynamic function of the angle of attack, Mach number and altitude; S2: determining a set of calculation conditions, including but not limited to the aerodynamic configuration, initial speed, and initial altitude of the aircraft; S3: Based on the dynamic model of the aircraft, according to the calculation conditions and aerodynamic functions, the maximum longitudinal range, minimum longitudinal range and maximum lateral range of the flight are solved under the constraints of terminal speed and altitude, and the reachable domain represented by relative longitude and latitude is generated; S4: performing the following processing on each group of calculation conditions determined in step S1: traversing the relative longitude and latitude of points in the reachable domain, taking the relative longitude and latitude as the terminal position constraint, solving the trajectory with the optimal terminal residual speed, and obtaining the capability envelope data of the aircraft under the calculation conditions, the capability envelope data including but not limited to the aircraft aerodynamic configuration, initial speed, initial altitude, target relative longitude, target relative latitude and the corresponding maximum residual speed of the aircraft; S5: Construct a capability envelope data set, perform feature selection and labeling on the capability envelope data, form a supervision data set in a unified format, and divide it into a training data set and a test data set; S6: Based on the training data set, establish and train an online prediction model for the capability envelope of a deformable aircraft, and perform supervised learning; S7: Based on the test data set, select test indicators and test the trained online prediction model of the deformable aircraft capability envelope; S8: Obtain the real-time speed, altitude, relative distance to the target and the angle of attack to the target of the deformable aircraft, input them into the online prediction model of the capability envelope of the deformable aircraft that has passed the test, and predict the maximum remaining speed of the aircraft in this state and target position.

2. The method for constructing a deformable aircraft capability envelope data set and predicting it online accurately according to claim 1, characterized in that: The Gauss pseudo-spectral method is used to calculate the reentry reachable domain. The angle of attack profile is not fixed. The angle of attack and the roll angle are simultaneously used as variables to be optimized to generate the reachable domain, which is as follows: In the polar coordinate system, the latitude and longitude of the starting point of the aircraft are both 0, and the longitude and latitude of the end point describe the longitudinal and lateral range of the aircraft respectively. The relative latitude and longitude information is used to characterize the position relationship between the missile and the target. The reentry reachable domain calculation method based on the Gauss pseudo-spectral method first solves the maximum and minimum longitudinal ranges L max and L min ; Then from the longitudinal L max -ΔL, solve the two maximum horizontal range problems respectively, and reduce the vertical range ΔL successively until it reaches L min , and obtain the maximum lateral trajectory under different longitudinal conditions; finally, the reentry reachable area of ​​the aircraft represented by relative longitude and latitude is obtained.

3. The method for constructing a deformable aircraft capability envelope data set and online accurate prediction according to claim 2 is characterized in that: Before calculating the reentry reachable domain calculation method based on the Gauss pseudospectral method, when setting the parameters of the pseudospectral method, the Coriolis acceleration term and the involved acceleration term in the differential equation are not 0, and the latitude variation range of the northern hemisphere trajectory is set to [-2°, 90°], and the latitude variation range of the southern hemisphere trajectory is set to [-90°, 2°].

4. The method for constructing a deformable aircraft capability envelope data set and online accurate prediction according to claim 1, characterized in that: The capability envelope data is calculated based on the Gauss pseudo-spectral method. The longitude and latitude of the points in the traversable domain are taken as terminal constraints. The maximum terminal residual speed is taken as the variable to be optimized to find the optimal trajectory of the terminal residual speed, that is, to obtain the capability envelope data of the aircraft at the current initial altitude and initial speed.

5. The method for constructing a deformable aircraft capability envelope data set and online accurate prediction according to claim 1, characterized in that: Feature selection and labeling are performed on the capability envelope data to form a unified format of supervision data set. The input features of the supervision data set are the initial speed of the aircraft, the initial altitude, the relative distance between the aircraft and the target, and the angle between the aircraft and the target. The output feature is the maximum residual speed of the aircraft under the above initial state and target position. Among them, the relative longitude and relative latitude in the capability envelope data are extracted for features: R=R e ·C In the formula, R e is the radius of the earth, λ is the relative longitude, is the relative latitude; R is the relative distance, and A is the direction angle, which are used as input features.

6. The method for constructing a deformable aircraft capability envelope data set and predicting it online accurately according to claim 1, characterized in that: The aerodynamic data of each shape of the aircraft are fitted, specifically: The aerodynamic data used are the basic aerodynamic data without rudder deflection, and the sideslip angle is zero, and the lateral force of the plane-symmetrical aircraft is zero; The fitting process is as follows: decompose the axial force coefficient and the normal force coefficient into the drag coefficient and the lift coefficient, and then use a cubic polynomial to fit them as a function of the Mach number and the angle of attack; fit the axial force coefficient increment as a function of the Mach number and the altitude; and finally obtain the aerodynamic function of the angle of attack, Mach number and altitude.

7. The method for constructing a deformable aircraft capability envelope data set and accurately predicting it online according to claim 1, characterized in that: The initial velocity sampling is performed on the nominal trajectory segment of the deformable aircraft to be predicted. The applicable speed range of different aerodynamic configurations is considered when selecting the trajectory velocity points. For the configuration that fails to cover all flight trajectory segments, its maximum allowable speed and the corresponding height on the nominal trajectory are taken as the initial state point.

8. The method for constructing a deformable aircraft capability envelope data set and online accurate prediction according to claim 1, characterized in that: Based on the polar coordinate system, the dynamic model of the aircraft is established, and the constraints of stagnation point heat flux density, overload constraint and dynamic pressure constraint are given. The above constraints are as follows: In the formula, is the heat flux density, is the heat flow calculation parameter, R N is the stagnation radius, ρ is the atmospheric density, ρ0 is the standard atmospheric density at sea level, v is the speed of the aircraft relative to the earth, V c is the first cosmic velocity, is the maximum heat flux density that the aircraft can withstand; g0 is the earth's gravitational acceleration, n max is the maximum aerodynamic overload that the aircraft can withstand; q is the dynamic pressure, q max is the maximum dynamic pressure; L and D are the lift acceleration and drag acceleration of the aircraft respectively.

9. The method for constructing a deformable aircraft capability envelope data set and predicting it online accurately according to claim 1, characterized in that: An online prediction model of the capability envelope of a deformable aircraft is established by using any supervised learning algorithm including but not limited to support vector machine, decision tree, multi-layer perceptron, and deep neural network. The initial speed, initial altitude, relative distance between the aircraft and the target, and the heading angle between the aircraft and the target are used as model inputs, and the maximum residual speed of the aircraft in the above initial state and target position is used as model output.

10. The method for constructing a deformable aircraft capability envelope data set and online accurate prediction according to claim 1, characterized in that: The trained online prediction model of the capability envelope of the deformable aircraft is tested. The test indicators are key indicators for measuring the regression model, including but not limited to the mean absolute error, root mean square error, square correlation coefficient, and determination coefficient.

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